Avoid anything lighter than 100gr.
The Hornady 100gr Interlok as loaded in the Hornady factory ammo is outstanding. At any range beyond 100yds It'll probably shoot broadside through any whitetail or mule deer.
The Remington 100 or 120gr Corlokt ammo is outstanding for the price. Either will perform well, but for closer in shots or large deer, the 120 will work better. The 100gr due to high velocity will not penetrate as well at closer ranges. I've used both the 100 and 120gr bullets from my .257Roberts in hand loads and they work equally well. For mule deer and any shot at an elk, the 120gr will be superior.
For elk, I would only use one load. That is the Federal factory 120gr Nosler Partition, but if 115gr Partition is available, I'd use it likewise. The bullets are almost identical, except the 115gr has a slightly higer ballistic coefficient, so shoots a tad flatter.
Likewise, the Hornady 117gr BTSpt is very, very good. It too "might" make muster as an elk round. But, it would be at its best on mule deer or bean-field shooting of whitetails.
Avoid the Nosler ballistic tips. They are too frangible for close ranges at the velocities of the .25/06. I've had my .257wbymag cause the 115gr bullets to fragment and not penetrate even on a 100lb whitetail doe. Likewise the 100gr bullet from my handloaded .257Roberts which closely duplicate the factory performance of the .25/06.